Some fancy pet doors require professional installation, but you can install most pet doors with only a drill, a screwdriver, and an instruction manual. Before you buy a pet door, make sure that it comes with an installation manual.
For most pet doors, and especially for the flap variety, installation basically requires you to cut a hole in your door (or window). Carefully measure the dimensions of the pet door, keeping in mind that the door seal needs to extend over the door, and then mark the two top corners. Drill holes at these marks, and then cut out the rectangle for the door. Drill any additional holes needed for screws, and screw in the door.
Depending on the material of your door, you can clean it using soap and water. You may also want to put a floor mat on the inside of the door to minimize the amount of dirt that your pets track into the house.